Summary of Pickleball Spin Experiment
Crawford Lindsey, Tennis Warehouse, San Luis Obispo, CA, 93401
November 1, 2022

#### Introduction

This is an abridged, nontechnical summary of the Total Pickleball University (TPU) experiment Pickleball Spin — The Role of Surface Roughness in Spin Generation. The experiment was performed because most players believe that surface roughness makes a large difference in spin. Well, it does ... sort of, sometimes ... well, errr, ummm, not really ... not like we imagine, anyway.

Here's the long story short: There is a maximum theoretical limit to friction-caused spin for any given incident ball with a given angle, velocity and spin, no matter what the surface roughness. And for most players with most paddles, that limit is achieved for most shots. In four scenes, here is why:

#### Scene 1: Impact With Linear Speed, No Spin

First, if a ball with speed v and no spin impacts a small bit obliquely on a paddle, it will first slide along the paddle and then stop due to the slowing and stopping force of friction. Friction always acts in the opposite direction of the ball's motion. As the incident angle becomes more and more oblique, the ball will slide a greater distance before it stops because it is travelling faster relative to the paddle's surface, even though the impact speed is the same. As the ball slides, friction both slows it and starts it spinning. At the bottom of the ball, the spin direction will be opposite to the slide direction. As the ball slows and the spin increases, there will come a time when the spin speed backwards will be equal and opposite to the slide speed forward. The two speeds will cancel, the bottom of the ball will no longer be moving across the paddle (zero contact speed), friction will thus stop, as will any further increase in spin, and the ball is said to "grip" the paddle. At this point the maximum possible spin has been achieved, regardless of the roughness of the paddle's surface. At angles where both a rough and a smooth paddle achieve the condition of zero contact speed, they will both produce the same spin.

As the impact angle becomes more and more oblique, and the incident sliding speed greater and greater, there usually will come an angle at which friction can't achieve it's goal of equal and opposite linear speed and spin speed. The ball will slide for the entire impact. If this occurs, the rough paddle will produce more spin than the smooth one, but neither will produce as much spin as when they gripped the surface.

#### Scene 2: Impact With Spin Speed, No Linear Speed

Second, if, instead, the incident ball impacts perpendicular to the paddle at the same speed v but with large spin, then the same process would occur. The bottom of the ball has no initial linear sliding speed but it is "sliding in place" in the spin direction, so friction acts to slow the spin speed and begin as well as increase linear speed in the opposite direction. The end is the same — equal and opposite linear and rotational contact speed as well as equal spin for all paddles up to the sliding-gripping transition angle for each paddle's surface roughness.

#### Scene 3: Impact With Linear and Spin Speed

And third, if, as is usually the case, the incident ball has both a linear and rotational speed at the contact point, then friction acts in a direction opposite the net speed of the separate incident contact motions. The result is the same — the same spin for all paddles up the the slide-grip transition angle, and rougher paddles producing more spin when sliding lasts throughout the impact duration.

#### Scene 4: Swing Impact Angles

The scenes above depict a slide-to-grip transition angle, above which all paddles generate the same spin and below which rough paddles produce more spin. But that is in the lab. On court, most ball striking takes place at angles above the transition. The actual impact angle is the net result of ball angle, swing angle, and paddle tilt, In other words, most ball striking is taking place under conditions where all paddles will produce the same friction-induced spin.

#### Conclusion/Rehash

Some people prefer lists to narrative, bullet points instead of a story. As such, by way of a conclusion, here you go ...

• Friction only influences spin when the ball is sliding across the paddle.
• Friction acts opposite the direction of sliding.
• Sliding direction depends on two factors: the linear speed and direction of the ball's movement and the linear speed and direction of the spin at the contact point.
• Linear and rotational speeds can be in the same or opposite directions and it is their net sum that determines contact sliding direction and thus friction direction.
• Friction acts to slow the ball and to change the spin, but it does so only as long as the contact point is sliding in one direction or the other.
• If the rotational contact speed becomes equal and opposite the linear contact speed, then there is no motion at the contact point and friction stops. At this point the ball "grips" the paddle
• When friction stops, spin generation stops.
• At large incident ball angles from the paddle surface, the linear ball velocity is low, there is not much sliding, so friction comes to a stop early in the impact.
• As incident angles get more oblique, there is more sliding, friction decreases but lasts longer, and more change in both linear and rotational speeds takes place before the ball grips the surface.
• Finally, at even more oblique angles to the surface, there is not enough friction to grip the ball, even though it acts throughout the impact duration.
• Sliding will occur for the entire impact duration.
• The rougher, higher friction paddle will generate more spin than the smooth one, but neither will generate as much spin as when the ball grips.
• The angle at which most swings impact the ball is in the gripping range of most paddles.
• Thus, most paddles for most swings produce the same spin.